Statement-1 : In compound pendulum, if suspension point and centre of oscillation are mutually inter change, then no change in time period is obtained.
Statement-2 : Length of equivalent simple pendulum remains same in both the case.

Options

A. Statement-1 is True, Statement-2 is True , Statement-2 is a corrrect explanation for Statement-1
B. Statement-1 is True, Statement-2 is True , Statement-2 is NOT a corrrect explanation for Statement-1
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

To solve the question, we need to analyze both statements regarding the compound pendulum and the equivalent simple pendulum.

### Step-by-Step Solution:

1. **Understanding the Compound Pendulum**:
- A compound pendulum consists of a rigid body that is free to oscillate about a horizontal axis. The time period of oscillation depends on the distance between the point of suspension and the center of mass.

2. **Interchanging Suspension Point and Center of Oscillation**:
- When the suspension point and the center of oscillation are interchanged, the distance between them remains the same. Let’s denote this distance as \(d\).

3. **Time Period of Compound Pendulum**:
- The time period \(T\) of a compound pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{m g d}{I}} \]
where \(m\) is the mass, \(g\) is the acceleration due to gravity, \(d\) is the distance from the pivot to the center of mass, and \(I\) is the moment of inertia about the pivot point.

4. **Effect of Interchanging Points**:
- Since the distance \(d\) remains unchanged when the suspension point and the center of oscillation are interchanged, the time period \(T\) will also remain unchanged.

5. **Equivalent Simple Pendulum**:
- The equivalent simple pendulum has a length \(L\) such that:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- The length \(L\) of the equivalent simple pendulum is determined by the same distance \(d\) that was used in the compound pendulum.

6. **Conclusion**:
- Since both the time period and the length of the equivalent simple pendulum remain the same when the suspension point and the center of oscillation are interchanged, both statements are true and the second statement correctly explains the first.

### Final Answer:
- Both Statement-1 and Statement-2 are true. Statement-2 is the correct explanation for Statement-1.